Quasidiagonal approach to the estimation of lyapunov spectra for spatiotemporal systems from multivariate time series

We describe methods of estimating the entire Lyapunov spectrum of a spatially extended system from multivariate time-series observations. Provided that the coupling in the system is short range, the Jacobian has a banded structure and can be estimated using spatially localized reconstructions in low embedding dimensions. This circumvents the "curse of dimensionality" that prevents the accurate reconstruction of high-dimensional dynamics from observed time series. The technique is illustrated using coupled map lattices as prototype models for spatiotemporal chaos and is found to work even when the coupling is not strictly local but only exponentially decaying.